In a December phone call with Saudi Arabia's King Salman, President Donald Trump had an idea he thought could hasten a U.S. exit from Syria: Ask the king for $4 billion. By the end of the call, according to U.S. officials, the president believed he had a deal.

The White House wants money from the kingdom and other nations to help rebuild and stabilize the parts of Syria that the U.S. military and its local allies have liberated from the Islamic State. The postwar goal is to prevent Syrian President Bashar Assad and his Russian and Iranian partners from claiming the areas, or the Islamic State from regrouping, while U.S. forces finish mopping up the militants.

The Saudis, whose crown prince arrives in Washington on Monday for extensive meetings with the administration, are part of the anti-Islamic State coalition but have largely withdrawn from the fight in Syria in recent years. They are questioning the eye-popping sum even as U.S. officials at one point were drawing up line items totaling $4 billion.

For Trump - who has long railed against insufficient burden-sharing by allies under the U.S. security umbrella - getting others to foot the bill for expensive postwar efforts is important.

A $4 billion Saudi contribution would go a long way toward U.S. goals in Syria that the Saudis say they share, particularly that of limiting Assad's power and rolling back Iran's influence. By comparison, the United States last month announced a $200 million donation to the stabilization effort.

At the same time, Trump is eager to get the United States out of a war in which he has already claimed that victory over the Islamic State is near. Boasting of the Islamic State's defeat in a speech Tuesday to U.S. troops in California, he said, "We knocked the hell out of them."

"We won't let up until ISIS is completely destroyed," Trump said, using an acronym for the militants. "ISIS never thought this would happen. They never got hit like this."

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Pentagon policy dating back to the Obama administration has limited U.S. involvement in the civil war in Syria almost exclusively to fighting the Islamic State through proxy forces backed by American troops.

The fight has been successful. But despite the rollback of Islamic State territory, the increasing likelihood of an Assad victory in the civil war has left many U.S. policymakers and lawmakers aghast and the U.S. mission in Syria jumbled and confused.

Gen. Joseph Votel, head of U.S. Central Command, which oversees the Middle East, was asked in congressional testimony Tuesday whether Assad, with Iranian and Russian help, had already won.

"I do not think that is too strong of a statement," Votel replied. "I think they have provided him with the wherewithal to be ascendant at this point."

The question is an important one, since the second phase of current U.S. strategy in Syria, after defeating the Islamic State, is to promote a political settlement of the war that ultimately includes the exit of both Assad and Iran.

U.S. commanders have said their military mission in Syria remains limited to defeating the Islamic State. But some administration officials have begun characterizing the U.S. presence more broadly, suggesting that it must serve as a bulwark against Iran, ensure stability in liberated territory and bolster American aims in any future political settlement.

Sen. Lindsey Graham, R-S.C., who has been aligned with more-hawkish members of the administration on Middle East policy, pressed Votel on the idea of expanding the mission beyond the Islamic State. He underscored the negative long-term impact that a win for Iran, Russia and Assad would have on U.S. allies such as Israel and Jordan.

"And it is not your mission in Syria to deal with the Iranian-Assad-Russia problem?" Graham asked Votel. "That's not in your 'things to do,' right?"

"That's correct, senator," Votel replied.

Votel declined to say whether he believed the U.S. military should be pursuing that broader objective. Asked whether it was still U.S. policy that Assad must leave power, Votel said: "I don't know that that's our particular policy at this particular point. Our focus remains on the defeat of ISIS."

Other officials have spoken of additional U.S. goals. Syrian stability cannot be achieved "with Assad in place," Nikki Haley, the U.S. ambassador to the United Nations, said last fall, and "Iran is not going to be in charge."

Administration officials have convinced Trump that the U.S. military cannot remove its troops from northern Syria in part because of Iran.

A senior U.S. official, one of several who discussed Syria policy on the condition of anonymity to speak candidly, said that "convincing arguments have been made that some bad entity is going to be there," including Iran. "That seems to have carried the day for the time being, but I don't think anybody wants an indefinite [U.S. military] presence" in Syria, least of all Trump.

The U.N.-led peace process has been close to moribund for years, and soon-to-depart Secretary of State Rex Tillerson said in January that the United States would not "make the same mistakes" the Obama administration made in 2011, when it withdrew troops from an unstable Iraq. "The departure of Assad" through a U.N.-led peace process, Tillerson said, "will create the conditions for a durable peace within Syria and security along the borders."

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While Trump has approved the expansion of U.S. forces in Syria since coming to office, he remains wary of any broader role and doesn't want the Americans to stick around for long. The roughly 2,000 troops currently deployed train, advise and often assist the main U.S. partner, the Syrian Democratic Forces (SDF), near the front lines. One U.S. official said that involvement should be reevaluated every 18 months.

Tillerson was fired by Trump this week and turned State Department management over to his deputy while he remains in office until March 31. While it's not clear whether Assad's fate or the longevity of U.S. troops in Syria were points of contention between Tillerson and Trump, starkly different views about prospects for Assad and the peace process remain within the administration.

One senior official said the SDF should cut a deal with the Syrian regime, given that Assad is ascending and there is little U.S. appetite to expand the military mission. The SDF shares Assad's goal of ridding Syria of opposition rebels, the Islamic State and Turkish forces.

A second senior administration official, however, completely rejected the notion that Assad is winning, saying the regime is "weaker than it has ever been, certainly in this half of the civil war."

"If we compare it to his pre-civil-war position, he controls about half or less of prewar territory, less than half of the arable land and far less than half of strategic resources like oil and gas," the official said. Those who say otherwise, the official added, are "misunderstanding the political process."

A third administration official expressed shock that any top U.S. official at this point would make that case. "Really?" this official asked.

"That might be true if you were to remove the Russians and the Iranians and Hezbollah," the Iranian-backed Lebanese Shiite militia that has been a decisive fighting force in Syria. Without them, Assad "would fall almost immediately."

But with them, the official said, Assad appears to be making strong progress, destroying evermore rebels in the west and expanding his territory eastward to within miles of where the SDF and its U.S. backers are still fighting the Islamic State.

The United States also is relying on the strained SDF to hold some 400 foreign Islamic State fighters detained during the battle in Syria. Many of the detainees are being held together in large rooms, according to a U.S. official, raising concern that they will network and launch what some worry could become "ISIS 2.0."

Some of the money the United States is requesting from allies such as Saudi Arabia would be used to ensure that detainees are transferred to a facility with individual cells, the U.S. official said.

Representatives at the Saudi Embassy in Washington did not respond to a question about the $4 billion request U.S. officials say Trump made to King Salman.

While it has rejected direct involvement in the Syrian civil war, the United States is the largest humanitarian donor, providing $8 billion over the years in aid for the millions in communities besieged by fighting or driven from their homes into refugee camps.